ToPos：基于测地线Voronoi分解的地形流形上的自动化最优定位
ToPos: Automated Optimal Positioning on Topographic Manifolds using Constrained Geodesic Voronoi Decomposition
- University of Oulu（奥卢大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
ToPos是感知地形流形的自动化最优定位框架，采用约束测地线Voronoi分解与黎曼NAG引擎，在非凸正弦流形上使最优表面积均衡分布提升约74%，可作为GIS微服务支撑相关应用。
AI中文摘要：
可靠的自主建图、环境采样、最后一公里物流及基础设施部署，均依赖空间参考站点（SRS）的最优表面积均衡分布。传统二维欧氏方法因忽略地形变化和物理障碍物，在高起伏环境中常失效，导致显著的平面畸变、空间聚类，以及目标被置于不可达或遮蔽区域，损害数据完整性与操作安全性。本文提出ToPos，一种感知地形流形的自动化最优采样框架。我们将地形视为嵌入三维欧氏空间的离散二维流形，用遵循实际表面几何的非欧氏测地线距离替代标准平面地图距离。点分布被建模为优化问题，采用约束测地线Voronoi分解，通过黎曼Nesterov加速梯度（NAG）引擎求解。该方法将目标位置限制在可行的“安全区域”，考虑不可通行坡度、植被、环境遮挡等因素。通过对非凸正弦流形的评估，我们表明ToPos利用测地线指标缓解了平面畸变，以Voronoi单元面积的变异系数（CV）衡量，最优表面积均衡分布提升约74%。该框架被设计为可用于地理信息系统（GIS）的微服务，以支持上述应用。
英文摘要：
Reliable autonomous mapping, environmental sampling, last-mile logistics, and infrastructure deployment depend on the optimal surface area-balanced distribution of Spatial Reference Sites (SRS). Conventional 2D Euclidean methods often fail in high-relief environments by neglecting topographic variations and physical obstructions. This leads to significant planimetric distortion, spatial clustering, and the placement of targets in inaccessible or shadowed regions, compromising both data integrity and operational safety. This paper introduces ToPos, an automated framework for TOPography-aware Optimal Sampling on topographic manifolds. We treat the terrain as a discrete 2-dimensional manifold embedded in 3D Euclidean space and replace standard flat-map distances with non-Euclidean geodesic distances that follow the actual surface geometry. The point distribution is formulated as an optimization problem using a Constrained Geodesic Voronoi Decomposition, solved via a Riemannian Nesterov Accelerated Gradient (NAG) engine. Our approach restricts target locations to a feasible "safe zone," accounting for non-traversable slopes, vegetation, environmental occlusions, etc. Through evaluations on non-convex sinusoidal manifolds, we show that ToPos mitigates planimetric distortion by utilizing geodesic metrics. This approach results in a $\sim$74% improvement in optimal surface area-balanced distribution, as measured by the coefficient of variation (CV) of the Voronoi cell areas. The framework is architected as a Geographic Information System (GIS)-ready micro-service to bolster the mentioned applications. Index Terms: Topographic Manifolds, Geodesic Voronoi Decomposition, Infrastructure Deployment, 3D Mapping, Spatial Sampling, and Non-Euclidean Optimization.
